How can we find find the input image which maximizes the class-probability for an ANN?
In deep networks there is actually a wide variety of solutions to the problem, but if you need to find one, any easy way to do this is just through normal optimization schemes
$$\hat x = argmin_x \ L(y,x)$$
where $L(y,x)$ is your loss function. Since ANN's are generally differentiable you can optimize this iteratively with some form gradient descent scheme:
$$x^{i+1} \leftarrow x^{i} - \lambda \nabla_{x^i}L(y,x^i)$$
where $\lambda$ is your learning rate.